The Control Handbook, Second Edition: Control System Advanced Methods

0436431 - ÚTIA 2015 RIV US eng M - Část monografie knihy
Kučera, Vladimír
Riccati Equations and their Solution.
The Control Handbook, Second Edition: Control System Advanced Methods. Control System Advanced Methods. Boca Raton: CRC Press, 2011 - (Lewine, W.), s. 14.1-14.21. Electrical Engineering Handbook. ISBN 978-1-4200-7366-9
Grant CEP: GA MŠMT(CZ) 1M0567
Výzkumný záměr: CEZ:AV0Z10750506
Institucionální podpora: RVO:67985556
Klíčová slova: Riccati equation * optimal control * solution
Kód oboru RIV: BC - Teorie a systémy řízení
http://library.utia.cas.cz/separaty/2011/TR/kucera-0436431.pdf

A Riccati equation, deriving its name from Jacopo Francesco, Count Riccati (1676–1754) [1], who studied a particular case of this equation from 1719 to 1724. For several reasons, a differential equation of the form of Equation 14.1, and generalizations thereof comprise a highly significant class of nonlinear ordinary differential equations. First, they are intimately related to ordinary linear homogeneous differential equations of the second order. Second, the solutions of Equation 14.1 possess a very particular structure in that the general solution is a fractional linear function in the constant of integration. In applications, Riccati differential equations appear in the classical problems of the calculus of variations and in the associated disciplines of optimal control and filtering
Trvalý link: http://hdl.handle.net/11104/0240183